benchmarkfcns.ackleyn3

benchmarkfcns.ackleyn3(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Ackley N. 3 function. SCORES = ackley3(X) computes the value of the Ackley N. 3 function at point X. ackley3 accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1 in which each row contains the function value for the corresponding row of X. Properties:

  • Global minimum: Approximately -219.1418

  • Location of global minimum: Approximately (0.68258, -0.36075)

  • Number of dimensions: 2

  • Recommended domain: x_1, x_2 ∈ [-32, 32]

  • Number of local minima: Numerous (the combination of exponential and

    trigonometric terms creates a very “bumpy” surface)

  • Number of global minima: 1

  • Convexity: Non-convex

  • Separability: Non-separable

  • Modality: Multimodal

  • Symmetry: Non-symmetric

  • Differentiable: Yes

For more information, please visit: benchmarkfcns.info/doc/ackleyn3fcn

Mathematical Definition

Visualization

ackleyn3 landscape